Refactoring to new file, introduction of negation (#63)

Co-authored-by: Eddie <eddie see email elsewhere>

Author: thecppzoo

inc/zoo/swar/associative_iteration.h

@@ -0,0 +1,258 @@
+#ifndef ZOO_SWAR_ASSOCIATIVE_ITERATION_H
+#define ZOO_SWAR_ASSOCIATIVE_ITERATION_H
+
+#include "zoo/swar/SWAR.h"
+
+namespace zoo::swar {
+
+/// \note This code should be substituted by an application of "progressive" algebraic iteration
+/// \note There is also parallelPrefix (to be implemented)
+template<int NB, typename B>
+constexpr SWAR<NB, B> parallelSuffix(SWAR<NB, B> input) {
+    using S = SWAR<NB, B>;
+    auto
+        shiftClearingMask = S{~S::MostSignificantBit},
+        doubling = input,
+        result = S{0};
+    auto
+        bitsToXOR = NB,
+        power = 1;
+    for(;;) {
+        if(1 & bitsToXOR) {
+            result = result ^ doubling;
+            doubling = doubling.shiftIntraLaneLeft(power, shiftClearingMask);
+        }
+        bitsToXOR >>= 1;
+        if(!bitsToXOR) { break; }
+        auto shifted = doubling.shiftIntraLaneLeft(power, shiftClearingMask);
+        doubling = doubling ^ shifted;
+        // 01...1
+        // 001...1
+        // 00001...1
+        // 000000001...1
+        shiftClearingMask =
+            shiftClearingMask & S{shiftClearingMask.value() >> power};
+        power <<= 1;
+    }
+    return S{result};
+}
+
+/// \todo because of the desirability of "accumuating" the XORs at the MSB,
+/// the parallel suffix operation is more suitable.
+template<int NB, typename B>
+constexpr SWAR<NB, B> parity(SWAR<NB, B> input) {
+    using S = SWAR<NB, B>;
+    auto preResult = parallelSuffix(input);
+    auto onlyMSB = preResult.value() & S::MostSignificantBit;
+    return S{onlyMSB};
+}
+
+
+namespace impl {
+template<int NB, typename B>
+constexpr auto makeLaneMaskFromMSB_and_LSB(SWAR<NB, B> msb, SWAR<NB, B> lsb) {
+    auto msbCopiedDown = msb - lsb;
+    auto msbReintroduced = msbCopiedDown | msb;
+    return msbReintroduced;
+}
+}
+
+template<int NB, typename B>
+constexpr auto makeLaneMaskFromLSB(SWAR<NB, B> input) {
+    using S = SWAR<NB, B>;
+    auto lsb = input & S{S::LeastSignificantBit};
+    auto lsbCopiedToMSB = S{lsb.value() << (NB - 1)};
+    return impl::makeLaneMaskFromMSB_and_LSB(lsbCopiedToMSB, lsb);
+}
+
+template<int NB, typename B>
+constexpr auto makeLaneMaskFromMSB(SWAR<NB, B> input) {
+    using S = SWAR<NB, B>;
+    auto msb = input & S{S::MostSignificantBit};
+    auto msbCopiedToLSB = S{msb.value() >> (NB - 1)};
+    return impl::makeLaneMaskFromMSB_and_LSB(msb, msbCopiedToLSB);
+}
+
+template<int NB, typename B>
+struct ArithmeticResultTriplet {
+    SWAR<NB, B> result;
+    BooleanSWAR<NB, B> carry, overflow;
+};
+
+
+template<int NB, typename B>
+constexpr ArithmeticResultTriplet<NB, B>
+fullAddition(SWAR<NB, B> s1, SWAR<NB, B> s2) {
+    using S = SWAR<NB, B>;
+    constexpr auto
+        SignBit = S{S::MostSignificantBit},
+        LowerBits = SignBit - S{S::LeastSignificantBit};
+    // prevent overflow by clearing the most significant bits
+    auto
+        s1prime = LowerBits & s1,
+        s2prime = LowerBits & s2,
+        resultPrime = s1prime + s2prime,
+        s1Sign = SignBit & s1,
+        s2Sign = SignBit & s2,
+        signPrime = SignBit & resultPrime,
+        result = resultPrime ^ s1Sign ^ s2Sign,
+        // carry is set whenever at least two of the sign bits of s1, s2,
+        // signPrime are set
+        carry = (s1Sign & s2Sign) | (s1Sign & signPrime) | (s2Sign & signPrime),
+        // overflow: the inputs have the same sign and different to result
+        // same sign: s1Sign ^ s2Sign
+        overflow = (s1Sign ^ s2Sign ^ SignBit) & (s1Sign ^ result);
+    using BS = BooleanSWAR<NB, B>;
+    return { result, BS{carry.value()}, BS{overflow.value()} };
+};
+
+
+template<int NB, typename B>
+constexpr auto negate(SWAR<NB, B> input) {
+    using S = SWAR<NB, B>;
+    constexpr auto Ones = S{S::LeastSignificantBit};
+    return fullAddition(~input, Ones).result;
+}
+
+/// \brief Performs a generalized iterated application of an associative operator to a base
+///
+/// In algebra, the repeated application of an operator to a "base" has different names depending on the
+/// operator, for example "a + a + a + ... + a" n-times would be called "repeated addition",
+/// if * is numeric multiplication, "a * a * a * ... * a" n-times would be called "exponentiation of a to the n
+/// power".
+/// The general term in algebra is "iteration", hence the naming of this function.
+/// Since * and "product" are frequently used in Algebra to denote the application of a general operator, we
+/// keep the option to use the imprecise language of "product, base and exponent".  "Iteration" has a very
+/// different meaning in programming and especially different in C++.
+/// There may be iteration over an operator that is not associative (such as quaternion multiplication), this
+/// function leverages the associative property of the operator to "halve" the count of iterations at each step.
+/// \note There is a symmetrical operation to be implemented of associative iteration in the
+/// "progressive" direction: instead of starting with the most significant bit of the count, down to the lsb,
+/// and doing "op(result, base, count)"; going from lsb to msb doing "op(result, square, exponent)"
+/// \tparam Operator a callable with three arguments: the left and right arguments to the operation
+/// and the count to be used, the "count" is an artifact of this generalization
+/// \tparam IterationCount loosely models the "exponent" in "exponentiation", however, it may not
+/// be a number, the iteration count is part of the execution context to apply the operator
+/// \param forSquaring is an artifact of this generalization
+/// \param log2Count is to potentially reduce the number of iterations if the caller a-priori knows
+/// there are fewer iterations than what the type of exponent would allow
+template<
+    typename Base, typename IterationCount, typename Operator,
+    // the critical use of associativity is that it allows halving the
+    // iteration count
+    typename CountHalver
+>
+constexpr auto associativeOperatorIterated_regressive(
+    Base base, Base neutral, IterationCount count, IterationCount forSquaring,
+    Operator op, unsigned log2Count, CountHalver ch
+) {
+    auto result = neutral;
+    if(!log2Count) { return result; }
+    for(;;) {
+        result = op(result, base, count);
+        if(!--log2Count) { break; }
+        result = op(result, result, forSquaring);
+        count = ch(count);
+    }
+    return result;
+}
+
+template<int ActualBits, int NB, typename T>
+constexpr auto multiplication_OverflowUnsafe_SpecificBitCount(
+    SWAR<NB, T> multiplicand, SWAR<NB, T> multiplier
+) {
+    using S = SWAR<NB, T>;
+
+    auto operation = [](auto left, auto right, auto counts) {
+        auto addendums = makeLaneMaskFromMSB(counts);
+        return left + (addendums & right);
+    };
+
+    auto halver = [](auto counts) {
+        auto msbCleared = counts & ~S{S::MostSignificantBit};
+        return S{msbCleared.value() << 1};
+    };
+
+    multiplier = S{multiplier.value() << (NB - ActualBits)};
+    return associativeOperatorIterated_regressive(
+        multiplicand, S{0}, multiplier, S{S::MostSignificantBit}, operation,
+        ActualBits, halver
+    );
+}
+
+/// \note Not removed yet because it is an example of "progressive" associative exponentiation
+template<int ActualBits, int NB, typename T>
+constexpr auto multiplication_OverflowUnsafe_SpecificBitCount_deprecated(
+    SWAR<NB, T> multiplicand,
+    SWAR<NB, T> multiplier
+) {
+    using S = SWAR<NB, T>;
+    constexpr auto LeastBit = S::LeastSignificantBit;
+    auto multiplicandDoubling = multiplicand.value();
+    auto mplier = multiplier.value();
+    auto product = S{0};
+    for(auto count = ActualBits;;) {
+        auto multiplicandDoublingMask = makeLaneMaskFromLSB(S{mplier});
+        product = product + (multiplicandDoublingMask & S{multiplicandDoubling});
+        if(!--count) { break; }
+        multiplicandDoubling <<= 1;
+        auto leastBitCleared = mplier & ~LeastBit;
+        mplier = leastBitCleared >> 1;
+    }
+    return product;
+}
+
+template<int NB, typename T>
+constexpr auto multiplication_OverflowUnsafe(
+    SWAR<NB, T> multiplicand,
+    SWAR<NB, T> multiplier
+) {
+    return
+        multiplication_OverflowUnsafe_SpecificBitCount<NB>(
+            multiplicand, multiplier
+        );
+}
+
+template<int NB, typename T>
+struct SWAR_Pair{
+    SWAR<NB, T> even, odd;
+};
+
+template<int NB, typename T>
+constexpr SWAR<NB, T> doublingMask() {
+    using S = SWAR<NB, T>;
+    static_assert(0 == S::Lanes % 2, "Only even number of elements supported");
+    using D = SWAR<NB * 2, T>;
+    return S{(D::LeastSignificantBit << NB) - D::LeastSignificantBit};
+}
+
+template<int NB, typename T>
+constexpr auto doublePrecision(SWAR<NB, T> input) {
+    using S = SWAR<NB, T>;
+    static_assert(
+        0 == S::NSlots % 2,
+        "Precision can only be doubled for SWARs of even element count"
+    );
+    using RV = SWAR<NB * 2, T>;
+    constexpr auto DM = doublingMask<NB, T>();
+    return SWAR_Pair<NB * 2, T>{
+        RV{(input & DM).value()},
+        RV{(input.value() >> NB) & DM.value()}
+    };
+}
+
+template<int NB, typename T>
+constexpr auto halvePrecision(SWAR<NB, T> even, SWAR<NB, T> odd) {
+    using S = SWAR<NB, T>;
+    static_assert(0 == NB % 2, "Only even lane-bitcounts supported");
+    using RV = SWAR<NB/2, T>;
+    constexpr auto HalvingMask = doublingMask<NB/2, T>();
+    auto
+        evenHalf = RV{even.value()} & HalvingMask,
+        oddHalf = RV{(RV{odd.value()} & HalvingMask).value() << NB/2};
+    return evenHalf | oddHalf;
+}
+
+}
+
+#endif